This project encompasses the development and evaluation of statistical methods appropriate for epidemiologic research. This year work has concentrated in two main areas. The first is statistical analysis of spatial and temporal clustering to investigate the etiology of disease, including the possible roles of environmental factors. The second is mathematical modelling of various aspects of reproduction. Of particular interest are models which can explicitly incorporate the effects of environmental insults. A list of specific developments follows. (1) A new measure of geographic clustering was proposed. (2) A new statistic for detecting seasonality of events (such as disease onset) was developed and characterized. This statistic is designed to be particularly sensitive to a pattern where three seasons have similar incidence but one has an increased incidence. (3) Proportional hazards type models for fertility were developed, based on the number of menstrual cycles required to achieve pregnancy. Using such models, we can assess the aggregated effects on fertility (and preclinical loss) of covariates including environmental agents. (4) An improved algorithm for identifying the time of ovulation using estrogen and progesterone levels was developed; this is a useful prerequisite for various other analyses. (5) A mathematical model has been proposed which can usefully be applied to data on early pregnancy loss in women undergoing in vitro fertilization/embryo transfer. This model exploits the fact that several embryos are transferred, in order to separate effects on the maternal uterus from effects on the zygotes. (6) In ongoing work, we are attempting to develop models for conception following intercourse on different days of the menstrual cycle. Currently, we are focusing on very simple models; potentially effects of environmental exposures on ovum viability and sperm lifetime could be estimated.